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Would a US law be binding on a Portuguese company?
Today, yes - in effect. In 2009, the UNESCO Convention on the Protection of Underwater Cultural Heritage finally came into effect. Portugal has ratified the Convention, even though the United States has not. This effectively enshrines in international law the doctrine that sunken naval vessels remain the property of the government of the country that commissioned them and cannot be excavated or disturbed without that government's permission.
This has led to some exploitation of loopholes. The Spanish government, for example, considers every single ship that sailed under the Spanish flag as a "Spanish warship", even if that vessel's primary purpose was a treasure barge. Which is why Spain goes after salvage companies and foreign governments that recover treasure from Spanish wrecks.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis